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Design Considerations of Resonant DC/DC
Converter for Fuel Cell Inverter Application
Aleksandrs Andreiciks (M.sc.ing., Riga Technical University), Oskars Krievs (Dr.sc.ing., Riga Technical University)
Abstract – In order to use hydrogen fuel cells in domestic
applications either as main power supply or backup source, their
low DC output voltage has to be matched to the level and
frequency of the utility grid AC voltage. Such power converter
systems usually consist of a DC-DC converter and a DC-AC
inverter. The paper focuses on double-stage, grid-connected Fuel
Cell conversion systems. Comparison of different structures of
resonant DC-DC converters, which allows reduced switching
losses, are analyzed accounting the specific behavior of Fuel
Cells. The converter is elaborated for 5 kW power to match the
rated power of the proton exchange membrane (PEM) fuel cell
Keywords – Fuel Cell System, LLC Resonant DC/DC
Converter
I. INTRODUCTION
The research of renewable energy resources, as well as the
hydrogen energy has gained a growing interest in the recent
years. The hydrogen fuel cells are fully ecological, taking into
account that heat and water are the only by-products, which
are excreted into the environment. The typical applications of
hydrogen fuel cells include electrical transport, combined heat
and power generation systems. In order to utilize the electrical
energy which is produced by the fuel cells, characterized by
slow dynamic response, low output voltage and large voltage
variations, static power converters are researched widely
throughout the world. [1]
The fuel cells used in domestic application, either as main
power supply or backup source, need to be connected to the
grid. Thereby, their low DC voltage has to be converted by
means of a power converter into AC voltage in accordance
with the grid voltage parameters. Such power converter
systems usually consist of a DC-DC converter and a DC-AC
converter. To reach a suitable DC voltage supply for the
inverter, it is necessary to use a transformer or a boost DC/DC
converter. When the required voltage amplification is large,
the boost topology is not appropriate due to the lack of
galvanic insulation between the input and output. In such
cases DC/DC converters with high frequency transformer are
preferred. In order to minimize the switching losses in high
frequency DC/DC converters, different topologies of resonant
converters have been investigated [2], [3] using the softswitching power conversion techniques.
Usually, the analysis of resonant converters considers their
employment in switching power supply applications where a
wide range of the ratio between input and output voltages is
required. In such scope, this paper provides a comparison
among the most promising resonant converter topologies.
Subsequently, a detailed simulation study of the most
appropriate resonant converter has been carried out to be used
for 5kW proton exchange membrane (PEM) fuel cell. The
proposed 5kW LLC resonant converter is designed for
boosting from the low input voltage (80Vdc-100Vdc) to high
output voltage (400Vdc), the predicted maximum efficiency is
η>95%.
II. RESONANT DC/DC CONVERTERS
In many years, it has been a world-wide trend to reduce the
volume of the switching power supplies by increasing the
switching frequency. However, the high frequency causes low
efficiency because of high switching losses. Since the resonant
converter has ZVS or ZCS function for reducing the switching
losses, the resonant converter has been widely used in the
power industry. Resonant DC/DC converters are constituted
by an inverter followed by a rectifier and an output filter.
Many structures may be employed to realize a resonant
DC/DC converter; the two basic structures are characterized
by a different position of the capacitor of the resonant circuit
that can be placed in series (Series Load Resonant, SLR), or in
parallel (Parallel Load Resonant, PLR) to the load. Other
structures, denoted as series parallel resonant converters,
employ two capacitors (LCC) or two inductances (LLC). [2]
A. Series Load Resonant Converter
The circuit diagram of a half-bridge Series Load Resonant
converter is shown in Fig. 1. The two inverter switches S1 and
S2 are alternatively turned on and off, with a suitable
switching frequency, ƒs. According to the value of the
switching frequency, the resonant converter can operate in
three different modes [2].
When ƒs is smaller than half of the resonance frequency ƒo
of the Lr Cr circuit:
f0 
1
.
2 Lr Cr
(1)
the inverter's conduction is of discontinuous type. In this
operating condition, the inverter switches turn off at zero
voltage and current and turn on with a limited current slope, so
S1
D1
Coss1
D3
Cr
+
Lr
n:1:1
VFC
np
S2
D2
Coss2
Co
nS
nS
Fig. 1. Half-bridge Series Load Resonant Converter
Ro
-
D4
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the switching losses are very small. However, due to the
discontinuous conduction, the current peak is greater than in
continuous conduction; therefore, the conduction losses
increase.
When ƒs is comprised between ƒo/2 and ƒo (ƒo/2<ƒs ≤ƒo)
the conduction is of continuous type. In this frequency region
the commutations of the inverter switches are similar to that
produced by a square wave commutating inverter with a
capacitive load; i.e. the turn off occurs at zero current (ZCS)
but the turn on happens at non-zero voltage and current, with
significant switching losses.[1]
Also when ƒs is greater than ƒo the conduction is of
continuous type. In this operating condition the commutations
of the inverter switches are similar to that produced by a
square wave commutating inverter with an inductive load; i.e.
the turn on occurs at zero voltage (ZVS) while the turn off is
characterized by significant switching losses. Nevertheless,
the turn off losses can be widely reduced by inserting a
suitable capacitor in parallel to each switch. In this way, both
the switching and the conduction losses are adequately small.
The characteristic factor Q is the ratio between the
characteristic impedance and the load. Fig. 2 shows, for
different values of characteristic factor, Q defined as:
Q
2f 0 Lr
.
Ro
(2)
The DC gain characteristic g is defined as:
g
Vo
.
Vin / 2
(3)
A ratio k between the switching frequency and the
resonance frequency is:
k
fs
.
f0
(4)
In the Fig. 2 the transformer ratio ns/ np has been assumed as
unitary. The DC gain characteristics are significant when the
resonant converter is used to supply a DC load with a
controlled voltage.
Fig. 2. DC gain characteristics of a SLR Resonant Converter
The series-resonant converter has the main disadvantage
that the output voltage cannot be regulated for the no-load
case. This can be seen from the characteristic resonant curves
of Fig. 2. At Q = 1, for example, the curves have very little
“selectivity,” and, in fact, at no load the curve would simply
be a horizontal line. This means that this converter would only
be used in applications where the load regulation is not
required. A mean to get some no-load regulation would be to
turn the converter on and off in a time ratio control fashion at
a frequency much lower than the resonant frequency of the
converter.
Another disadvantage of a converter is that the output dc
filter capacitor must carry high ripple current. This is a
significant disadvantage for applications with low output
voltage and high current. For this reason the series resonant
converter is not considered suitable for low output voltage
high output current converters but is it rather more suitable for
high-output-voltage low output current converters.
B. Parallel Load Resonant Converter
The circuit diagram of a half-bridge Parallel Load Resonant
Converter is shown in Fig.4. The behavior of the conversion
system is quite similar to the previous one as concern the three
operation modes. On the contrary, the DC gain characteristics
are very different, as shown in Fig. 3. From these curves it is
seen that, in contrast to the series-resonant converter, the
converter is able to control the output voltage at no load by
running at a frequency above resonance. Note also that the
output voltage at resonance is a function of load and can rise
to very high values at no load if the operating frequency is not
raised by the regulator [1].
The main disadvantage of the parallel-resonant converter is
that the current carried by the power MOSFETs and resonant
components is relatively independent of load. This converter is
less appropriate for applications which have a large input
voltage range and which require it to operate considerably
below its maximum design power while maintaining very high
efficiency. Conversely, the converter is better suited to
applications which run from a relatively narrow input voltage
range and which present a more or less constant load to the
converter near the maximum design power. Of course, the
power converter must be designed thermally for the maximum
power and, therefore, has no problem running at reduced
power thermally only the part load efficiency is less than the
full load efficiency. The parallel-resonant converter is suitable
for low output-voltage high output current applications. This is
due to the fact that the dc filter on the low-voltage output side
of the transformer is of the inductor input type and, therefore,
dc output capacitors capable of carrying very high ripple
currents are not needed. The inductor limits the ripple current
carried by the output capacitor. Note also that the transformer
leakage inductance could be used as the resonant inductance
by placing the resonant capacitor across the total span of the
secondary winding. This is normally not ideal for low output
voltages because the capacitor would have to carry too much
ac current. However, for higher output voltage converters this
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S1
C
D1
D3
Coss1
S1
Lo
n:1:1
VFC
Cr
np
Co
nS
nS
D2
Coss1
D3
Ro
Cr
+
Lr
n:1:1
VFC
D4
np
C
S2
D1
+
Lr
S2
Coss2
D2
Coss2
Lm
Co
nS
nS
Ro
-
D4
Fig. 3. Half-bridge Parallel Load Resonant Converter
Fig. 5. LLC Resonant Converter.
Fig. 4. DC gain charactericteristics of a PLR Resonant converter.
Fig. 6. DC gain charactericteristics of a LLC Resonant converter.
placement of the resonant capacitor may be desirable. Also,
the resonant capacitor can be placed on a tertiary transformer
winding [6].
LLC converter displays many advantages over other
resonant converter topologies; it can regulate the output over
wide line and load variations with a relatively small variation
of switching frequency, it can achieve zero voltage switching
(ZVS) over the entire operating range, and all essential
parasitic elements, including junction capacitances of all semiconductor devices and the leakage inductance of the
transformer, are utilized to achieve soft-switching [2].
C. LLC Resonant Converter
The circuit diagram of a half-bridge LLC Resonant
Converter is shown in Fig. 5. The behavior of the LLC
conversion system is quite similar to that of the SLR as
concern the three operation modes, but this circuit presents
two different resonance frequencies. When diode D3 or D4 are
turned on, resonant circuit becomes composed by Lr and Cr ,
so resonance frequency is equal to f0:
1
f0 
.
2 Lr Cr
(5)
On the contrary, when both diodes are open, inductance Lm
is in series to Lr ; therefore the resonance frequency becomes
equal to f1 :
f1 
1
.
2 ( Lr  Lm )Cr
(6)
Fig. 6 shows the DC gain characteristic g of the LLC
resonant converter assuming a value of Lm equal to that of Lr .
Comparing with SRC, the converter can achieve both Buck
mode and Boost mode. When the switching frequency is
higher than resonant frequency, voltage gain of LLC converter
is always less than one, and it operates as an SRC converter
and zero voltage switching (ZVS) can be achieved. When the
switching frequency is lower than resonant frequency, for
different load conditions, both ZVS and zero current switching
(ZCS) could be achieved. At the boundary of ZVS and ZCS
regions, converter voltage gain reaches it maximum value.
III. OPERATIONAL PRINCIPLES OF LLC RESONANT DC/DC
CONVERTER
As shown in Fig. 5, the primary switches S1 and S2 conduct
alternately to generate a symmetrical square waveform with
the magnitude of Vin/2. D1 (D2) and COSS1 (COSS2) are the antiparalleled diode and the equivalent output capacitor of S1 (S2).
The resonant tank is formed by the resonant capacitor Cr, and
the leakage inductor Lr and magnetizing inductor Lm of
transformer. The center-tapped rectifier is constructed by
connecting diodes D3 and D4 to the secondary windings of
transformer.
The main theoretical waveforms of the LLC resonant
DC/DC converter are shown in Fig. 7. There are ten operation
modes within one switching period. Because the waveforms
are symmetrical, only the operation principles of the first five
modes are introduced referring to the equivalent circuits
shown in Fig. 8. The operation principles of modes 6 to 10 are
similar [3].
A. Mode 1
This mode starts when the switch S1 is turned on under
ZVS. As shown in Fig. 8(a), the resonant current iLr is sinewave and increases from negative to discharge Cr, and energy
returns to the input power source. The voltage of Lm is
clamped to nVO so that the magnetizing current iLm increases
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Lm is in series with Lr and participates in the resonance with Cr
in the resonant tank. Because the equivalent inductance of (Lr
+ Lm) is much higher than Lr, as shown in Fig. 7, iLr and iLm are
almost constant in this short time interval.
F. Mode 5
While S1 is turning off, the resonant current iLr is charging
COSS1 and discharging COSS2 simultaneously. At the moment of
vds2 decreasing to zero, the resonant current iLr flows through
anti-paralleled diode D2 which provide ZVS operation for S2
turn-on. At the same time, the secondary rectifier diode D4
turns on. The voltage of Lm is clamped to nVO with reverse
polarity so that the current iLm decreases linearly. The
magnetizing inductor Lm is separated from the resonance with
Cr. When S2 turns on under ZVS, this mode ends and enters
the half cycle with symmetrical operation principles.
S1
D1
Coss1
D3
iL
+
r
n:1:1
VFC
S2
D2
Cr
Coss2
Fig. 7. Main waveforms of the LLC resonant converter operating with
frequency ratio between f0 and f1.
D1
nS
iL
D4
m
D3
+
r
n:1:1
VFC
S2
D2
Cr
Coss2
Lr
`
iL
3
Co
Ro
nS
np
Lm
iD
nS
D4
m
(b) Mode 2
S1
D1
Coss1
D3
+
iL
r
n:1:1
VFC
S2
D2
Cr
Coss2
C. Mode 2
As shown in Fig. 8(b), since iLr increases from zero to
positive, the input power source charges Cr and Lr, and
supplies energy to output load simultaneously. The energy in
Lm is released to output load continuously. When iLm reaches
zero, this mode ends.
Ro
Coss1
iL
B. Mode 1
This mode starts when the switch S1 is turned on under
ZVS. As shown in Fig. 8(a), the resonant current iLr is sinewave and increases from negative to discharge Cr, and energy
returns to the input power source. The voltage of Lm is
clamped to nVO so that the magnetizing current iLm increases
linearly from negative. The energy stored in Lm will be
released through D3 to output load. When iLr reaches zero, this
mode ends.
Co
nS
np
Lm
3
(a) Mode 1
S1
linearly from negative. The energy stored in Lm will be
released through D3 to output load. When iLr reaches zero, this
mode ends.
Lr
iD
Lr
iL
3
Co
Ro
nS
np
Lm
iD
nS
D4
m
(c) Mode 3
S1
D1
Coss1
D3
+
iL
r
n:1:1
VFC
S2
D2
Cr
Coss2
Lr
3
Co
Ro
nS
np
Lm
iD
nS
iL
D4
m
D. Mode 3
At this mode, because the voltage of Lm is still clamped to
nVO, iLm remains linearly increasing. The input power source
charges Lm and supplies energy to output load. The equivalent
circuit is shown in Fig. 8(c).
(d) Mode 4
S1
D1
Coss1
D3
iL
+
r
n:1:1
VFC
E. Mode 4
This mode starts when iLr and iLm equal each other. Current
circulating through the secondary diode D3 naturally decreases
to zero, and this diode turns off under ZCS condition. The
voltage spike caused by diode reverse recovery would not
exist. The voltage of Lm is no longer clamped to nVO, hence,
S2
D2
Cr
Coss2
Lr
np
Lm
iL
iD
nS
nS
3
Co
Ro
-
D4
m
(e) Mode 5
Fig. 8. Equivalent circuits of different modes for LLC converter operating
with frequency ratio between f0 and f1.
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Since Pin=Po/η, where η is the efficiency, we have:
IV. DESIGN SPECIFICATIONS AND CONSIDERATIONS
Based on the previous analysis, the practical design
procedure is presented in this section. It discusses optimizing
the resonant network for given input/output specifications.
The LLC resonant converter design goal is to achieve
minimum loss with the capability of achieve required
maximum gain to ensure wide operation range. The resonant
components including Lr, Cr, and Lm are the major task in
design considerations.
When the switching frequency is lower than resonant
frequency, there exists a flat im(t) in dead zone for ZVS while
the load viewed at primary side is infinite impedance. For ease
of analysis, the currents iL(t), im(t) and ip(t) are modeled as
shown in Fig. 9. The resonant inductor current iL(t) is
described as a linear combination of im(t) and ip(t), where ip(t)
is a sine waveform and im(t) a cosine wareform in stead of
triangular one. Interestingly, im(t) and ip(t) are orthogonal each
other [4].
From Fig. 8(a) we have
iL (t )  im (t )  i p (t ) ,
Po


I o2 RL


Vdc I o
,
2n
(11)
and the turns ratio n is then given by:
n
VDC  VDC

.
2 I o RL 2 Vo
(12)
The ZVS behavior during the dead time Fig. 8(e), in which
ip(t)=0, iL(t)=im(t)≈constant and Coos1=Coos2=Co. The required
time tZVS for ZVS is then given by:
t ZVS 
8Co LmVDC
.
nVoTS
(13)
and the maximum magnetizing inductance Lm can then be
estimated by, from (12), (13).
(7)
Lm 
nVoTS td ,min TS td ,min

.
8CoVDC
16Co
(14)
where
i p (t ) 
I o
2n
sin(  s t ) ,
(8)
From (10), the charge QCr in the resonant capacitor Cr at
resonance can be given by:
QCr  Cr QrVDC 
and
im (t ) 
nVo Ts
 cos(s t ) ,
Lm 4
(9)

VDC
TS

Vdc I o
2n
TS / 2

0
 I o 

 nV T 
 sin( S t )   o S  cos( S t ) dt

2
n
L
4

 m


 .
I oTS
2nQrVDC
(10)
(16)
and
Lr  Cr (n 2 RLQr ) 2 .
Pin  VDC iL ,av
(15)
and we have
Cr 
where n=Np/Ns is the turns ration. In Fig. 8(a) the power
drawn from supply Vdc occurs when S1 conducts during
0<t<Ts/2, i.e.
I oTS
,
2n
(17)
Due to practical considerations for the converter
components, the initial switching frequency fs is presumed to
be below fr for working in boost condition, we set fr = 100kHz.
From (12), the turns ration is given by n=Np/Ns= 0.11875/1. A
power MOSFET IRF 3077Pbf is employed as switch, with
Coos1=Coos2=Co=830pF. The dead time between two gate
drives is defined as 200ns. From (14), we can estimate the
magnetizing inductance to be Lm< 1430μH. From (16), we can
obtain Cr=7.46μF for Qr=0.3. The correspondent resonant
inductances are Lr=339 nH
V. SIMULATIONS
Fig. 9. Equivalent current waveform model for iL(t), im(t) and ip(t) in LLC
resonant converter.
To describe the operation of the LLC resonant converter
for fuel cell application, simulation results were obtained
using PLECS simulation software Fig. 10. shows a model of a
5 kW converter with 100 kHz switching frequency. Scopes are
connected to measure resonant output voltage, driving pulses
and load voltage. Waveforms are presented in the following
The header is left blank
order: gating signals; output of the inverter; resonant tank
circuit output voltage; output of the rectifier and load voltage.
As can be seen from the simulation rights the converter
operates as desired, providing 400 V output voltage at rated
input and load conditions.
VI. CONCLUSIONS
Fig. 10. LLC Converter schematics in PLECS environment
Fig. 11. Simulated waveforms of the LLC converter at full-load and 100Vdc
input, from the top – S1, S2 control voltage, current through Lr and Lm,
voltage of the resonant capacitor Cr..
In this paper, the design considerations for LLC resonant
converter for fuel cell application are explored. The analyzed
converter offers many advantages over other resonant
converter topologies; it can control the output over wide line
and load variations with a relatively small variation of
switching frequency, it can achieve zero voltage switching
over the entire operating range and all essential parasitic
elements, including junction capacitances of all semiconductor devices and the leakage inductance of the
transformer, are utilized to achieve soft-switching.
The voltage gain characteristics were analyzed based on the
theoretical analysis and computer simulation, which has
confirmed the conducted analysis. Every switching component
is operated in the soft switching condition of ZVS state for
primary MOSFET switches and ZCS state for secondary
diodes. The achieved results will be used for future work in
elaboration of laboratory prototype of the LLC resonant
converter.
REFERENCES
[1]
[2]
[3]
[4]
[5]
[6]
Fig. 12. Simulated waveforms of the LLC converter at full-load and 100 Vdc
input, from the top – D3, D4 current, output voltage, output current.
Fig. 13. Simulated waveforms of the LLC converter at no-load and 100Vdc
input, from the top – D3, D4 current, output voltage, output current.
L. Robert and A. Steigerwald, “A Comparison of Half-bridge resonant
converter topologies,” IEEE Transactions on Power Electronics, Vol. 3,
No. 2, April 1988.
J. F. Lazar and R. Martinelli, “Steady-State Analysis of the LLC Series
Resonant Converter,” in IEEE APEC’01, 2001, vol. 2, pp. 728-735.
Guan-Chyn Hsieh, “Design Considerations for LLC Series-Resonant
converter in two-resonant regions” in PESC, 2007, pp. 731-736.
G. Hsieh, “Design Considerations for LLC Series-Resonant converter in
two-resonant regions” in PESC, 2007, pp. 731-736.
B. Lu, W. Liu, Y Liang, Fred C. Lee, D. Jacobus and Van Wyk,
“Optimal design methology for LLC Resonant Converter,” APEC 2006,
pp.533-538
A. Bellini, S. Bifaretti and V. Iacovone, “Resonant DC-DC converters
for photovoltaic energy generation systems” SPEEDAM 2008, pp.815820
A. Andreiciks was born in Riga, Latvia, in 1985.
He received the B.sc.ing. and M.sc.ing degree at
Riga Technical University, Riga, Latvia in 2006 and
2008, respectively. Currently he is working towards a
PH.D. degree in Riga Technical University, Riga,
Latvia
He is currently an scientific assistant in the
Institute of Industrial Electronics and Electrical
Engineering, Riga Technical University. His main
field of interest is the design and optimization of
power electronic circuits for renewable energy
systems.
O. Krievs has received Bachelor’s (2001),
Master’s (2003) and Doctor’s (2007) degrees in the
field of electrical engineering at the Faculty of Power
and Electrical Engineering of Riga Technical
University. O. Krievs has been working in Riga
Technical University since 2001 and currently is in
the positions of assistant professor and leading
researcher at the Department of Power and Electrical
Engineering of Riga Technical University. His main
research fields include active power filters, frequency
converters and DC/DC converters.